A higher order model for image restoration: the one dimensional case

TL;DR

This paper analyzes a one-dimensional higher order total variation model for image restoration, establishing a functional framework for well-posedness and demonstrating that the higher order regularization prevents staircase artifacts.

Contribution

It introduces a functional framework ensuring well-posedness and proves that higher order regularization avoids staircase effects in one-dimensional image restoration.

Findings

The model is mathematically well-posed.

Higher order regularization prevents staircase artifacts.

Analytical proof of regularization benefits.

Abstract

The one-dimensional version of the higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [4] is analyzed. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the higher order regularizing term prevents the occurrence of the staircase effect.